A combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites

• A new incremental secant meanfield homogenization process for composites is proposed.
• The composite materials constituents follow elasto-plastic behaviors.
• The plastic residual strains in the different phases are piece-wise continuous.
• The matrix tangent operator used in the Eshelby tensor is intrinsically isotropic.
• The method predicts accurate results, for a broad range of composites and loading.

This paper presents an incremental secant mean-field homogenization (MFH) procedure for composites made of elasto-plastic constituents. In this formulation, the residual stress and strain states reached in the elasto-plastic phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using secant tensors, which are naturally isotropic and enable to define the Linear–Comparison-Composite. The method, which remains simple in its formulation, is valid for general non-monotonic and non-proportional loading. It is applied on various problems involving elastic, elasto-plastic and perfectly-plastic phases, to demonstrate its accuracy compared to other existing MFH methods.